aka Cell Death. Apoptosis is a process where a cell is degraded in order for it to be ultimately engulfed and recycled. Apoptosis can occur when a cell has become mutated and is on the verge of becoming a cancer. Apoptosis is also the reason why we don't have webbed hands and feet.
What basically happens is that the killer t cell communicates with the diseased cell by adhering to it by binding its death ligand to the death receptor on the diseased cell. This causes adapter proteins to attach to the cytosolic side of the receptor. This leads to a signal cascade which involves the recruitment of various other proteins and ultimately results in the death of the cell.